Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand
Conservative-Markdown Redirect-UCB Pricing achieves optimal Õ(T^{2/3}) regret for contextual dynamic pricing with agnostic non-Lipschitz demand, closing the prior regret gap.
Published 2026Atlanta Poster Session 4 · Thu, Dec 10, 4:30 PM–7:30 PM local time · Hall C1arXiv ↗OpenReview ↗
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Abstract
We study contextual dynamic pricing with linear valuations and bounded-support agnostic noise, whose induced demand curve may be non-Lipschitz with arbitrary jumps and atoms. Such discontinuities break the cross-context interpolation arguments used by smooth-demand pricing algorithms, while the best previous method achieved only $\tilde O(T^{3/4})$ regret. We propose Conservative-Markdown Redirect-UCB Pricing, a polynomial-time algorithm that combines randomized parameter estimation, conservative residual-grid probing, and confidence-based one-step redirection. Our algorithm achieves $\tilde O(T^{2/3})$ optimal regret, matching the known lower bounds of Kleinberg and Leighton (2003) up to logarithmic factors and improving over the previous upper bound of Xu and Wang (2022). Under stochastic well-conditioned contexts, this closes the long-existing open regret gap in linear-valuation contextual pricing under agnostic non-Lipschitz noise distribution.